lecture 2: electromagnetic radiation (aka the nature of...
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Lecture 2: Electromagnetic Radiation (aka The Nature of Light)
stationary charge has electric field
accelerating charge produces ripples (waves) in electric field
propagation direction perpendicular to E, B fields (E and B perpendicular too)
H = B field in this plot
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Five Fundamental Properties
a) speed of propagation, c
b) direction of propagation
c) wavelength
d) polarization (direction !E points)
light from source generally mixture of waves with different b), c), and d) properties
however, c is always cm/sec in vacuum3× 1010
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e) intensity
grows as magnitudes of !E and !B grow
one measure is energy/volume:
energy density =1
8π( "E ·
"E + "B ·"B)
=1
8π(E2 + B
2)
another measure is energy flux (energy crossing in some direction/area/time):
!f =c
4π( !E × !B)
f = cEB/4π
flux = c(energy density)
Poynting’s formula
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Sidebar: Vector Arithmetic
!A ·!B = ABcosθ
!A
θ
dot product
project length A onto direction B and multiply result
commutative : !A ·!B =
!B ·!A
If !A ⊥ !B, what does !A · !B =?
!B
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Sidebar: Vector Arithmetic
cross product
| !A × !B| = ABsinθ
!A
!B
!A × !Bθ
magnitude = area of parallelogram, direction given by right-hand rule
not commutative: !A × !B "= !B × !A
If !A ‖ !B, what does !A × !B =?
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The Nature of Light (cont.)
How does a charged particle respond to light?
force exerted on charge q moving at !v through !E, !B
!F = q( !E +!v
c× !B)
from !F = m!a, get !a ∝ q/m
electron oscillates sympathetically with passing EM wave
electron’s oscillation generates waves that reinforceor interfere (refraction or reflection)
why are mirror surfaces made of metal?
Lorentz’s formula
highest a for electrons
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Telescopesobservations by collecting and analyzing light
a photon's journey...
• emitted by a source (such as a star)
• perhaps absorbed by interstellar material along the way, perhaps re-emitted...
• crashes through atmosphere, perhaps absorbed (sunsets are red), perhaps scattered (the daytime sky is blue)
• falls onto telescope mirror (bounces on several mirrors)
• is seen by our eye, photographed, or digitally imaged
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key points of detecting radiation
• atmosphere limits light that reaches group by absorbing and scattering it, and also blurs image
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• telescopes collect light
• optics are used to reflect, refract, or disperse light
• at present, large optical telescopes can improve resolution up to few tenths of an arcsecond
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• instruments (computers and detectors) enable photometry and spectroscopy, large and sophisticated on modern telescopes...
• and running them and telescope is computer-intensive activity...
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• other ground based observing facilities in infrared and radio wavelength regimes...
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• space-based observatories remove constraints of atmosphere (blurring and blocking of certain wavelengths of light)
Hubble Telescope image
ground-based image
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1/r2Laws
gravity, electric force, light
let’s look at a radiating source
same amount of energy/time, or luminosity (L) crosses successive spheres at larger r
energy/area/time (energy flux) at distance r = L/4πr2
or, luminosity/surface area
standard candles --> distances